How do you verify the identity $tan (\frac{u}{2}) = csc u - cot u$ $tan(u/2)=cscu-cotu$ ?

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Answer 1 · 2017-11-09T13:53:29

See below.

$tan (\frac{u}{2}) = \frac{1 - cos u}{sin u}$ $tan(u/2)=(1-cosu)/sinu$ (Identity)

$\frac{1 - cos u}{sin u} = \frac{1}{sin u} - \frac{cos u}{sin u}$ $(1-cosu)/sinu= 1/sinu - cosu/sinu$

$\frac{1}{sin u} = csc u$ $1/sinu=cscu$

$- \frac{cos u}{sin u} = - cot u$ $- cosu/sinu= -cotu$

$:.$

LHS

$cscu-cotu$

$LHS-=RHS$

How do you verify the identity tan(u/2)=cscu-cotutan(u2)=cscu−cotutan(u/2)=cscu-cotu?